This project will continue the development of statistical methodology useful in the design and analysis of studies involving censored survival data. Emphasis will also be given to the evaluation of the large and small sample behavior of newly proposed procedures and of other existing techniques. Methods used will include asymptotic theory for statistical tests, Monte Carlo simulations, and numerical analysis. In the area of linear and non-linear rank test procedures, four important issues will be addressed: (a) the development and evaluation of K-sample omnibus test procedures based upon non-linear rank supremum-type statistics; (b) development and evaluation of one-sample tests of location which can be employed in the two-sample match pair survival problem involving possibly unequal censoring distribution; (c) evaluation of efficiencies and general properties of a board class of linear rank statistics which include the log rank, Pto-Peto Wilcoxon, and Harrington-Fleming Gp class as special cases; and (d) the investigation of large and small sample properties of previously and newly proposed rank statistics when sample sizes or censoring distributions are unequal. Large and small sample properties of the Cox proportional hazards regression model will also be investigated. Special attention will be given to the effects of: (a) over or under parameterization of the model, (b) heterogeneity in the data, and (c) model reduction techniques. Finally, a formal study of the large sample efficiencies of recently proposed group sequential linear rank procedures will be performed.